applying armature scale yield to change object location
As you can see your armature has a pose, it has been moved away from its origin and keyframed in Pose mode. If you apply the scale in Object mode, the bones will keep this distance from the origin but, as the armature has been scaled down, the distance will be scaled up as much. So what you need to do before applying the scale is go in Pose mode and reset the pose with an AltG.